Question

If x = 10, which lines are parallel? Check all that apply.

Lines b, c, d, e are cut by transversal a. Clockwise from top left, the angles formed by lines b and a are blank, (7 x minus 5) degrees, blank, blank; by lines c and a are blank, blank, (10 x + 15 degrees), blank; by lines d and a are (12 x minus 5) degrees, blank, blank, blank; by lines e and a are blank, (8 x minus 25) degrees, blank, blank.
b is parallel to c
b is parallel to d
b is parallel to e
c is parallel to d
c is parallel to e
d is parallel to e

Answer 1

To determine which lines are parallel, we need to consider the corresponding angles formed by the transversal and the lines. For lines to be parallel, the corresponding angles must be equal, or the alternate interior angles must be equal.

Given the angles:
- **Line b**: angles formed are blank, (7x - 5)°, blank, blank
- **Line c**: angles formed are blank, blank, (10x + 15)°, blank
- **Line d**: angles formed are (12x - 5)°, blank, blank, blank
- **Line e**: angles formed are blank, (8x - 25)°, blank, blank

Substituting \( x = 10 \):
1. For line b:
- Angle = \( 7(10) - 5 = 70 - 5 = 65° \)

2. For line c:
- Angle = \( 10(10) + 15 = 100 + 15 = 115° \)

3. For line d:
- Angle = \( 12(10) - 5 = 120 - 5 = 115° \)

4. For line e:
- Angle = \( 8(10) - 25 = 80 - 25 = 55° \)

Now we have the angles related to the lines:
- Line b: 65°
- Line c: 115°
- Line d: 115°
- Line e: 55°

Now we can check which pairs of lines are parallel:

- **b and c**: 65° and 115° are not equal. Not parallel.
- **b and d**: 65° and 115° are not equal. Not parallel.
- **b and e**: 65° and 55° are not equal. Not parallel.
- **c and d**: 115° and 115° are equal. Parallel.
- **c and e**: 115° and 55° are not equal. Not parallel.
- **d and e**: 115° and 55° are not equal. Not parallel.

From this, we conclude that the only lines that are parallel are:

- **c is parallel to d**.

So, the answer is:
- c is parallel to d.